First note that, by [1]}, \(M\)  is \((n+1)\) -torsionfree, i.e., \(\operatorname{Ext}^i_R(\operatorname{Tr}M,R)=0\)  for all \(i=1, \ldots , n+1\)  Consequently, \(M\)  is reflexive and \(\operatorname{Ext}^i_R(M^*,R)=0\)  for all \(i=1, \ldots , n-1\) . By our assumption, \(\operatorname{\textnormal {grade}}_R(\operatorname{Tor}_i^R(M,M^*))\ge n\)  for all \(i\ge 1\) . Now the assertion is clear by Lemma REF .
